Korean J. Math.  Vol 26, No 3 (2018)  pp.373-385
DOI: https://doi.org/10.11568/kjm.2018.26.3.373

Fuzzy homomorphism theorems on groups

Gezahagne Mulat Addis

Abstract


In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.


Keywords


Fuzzy mappings; fuzzy homomorphisms; fuzzy normal subgroups; quotient groups induced by fuzzy normal subgroups; fuzzy isomorphism theorems

Subject classification

03E72, 08A72, 20A99

Sponsor(s)



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